Basic Math Examples

$| 4 w + 6 | = 14$

Step 1

Remove the absolute value term. This creates a

$\pm$ on the right side of the equation because

$| x | = \pm x$ .

$4 w + 6 = \pm 14$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

Step 2.1

First, use the positive value of the

$\pm$ to find the first solution.

$4 w + 6 = 14$

Step 2.2

Move all terms not containing

$w$ to the right side of the equation.

Tap for more steps...

Step 2.2.1

Subtract

$6$ from both sides of the equation.

$4 w = 14 - 6$

Step 2.2.2

Subtract

$6$ from

$14$ .

$4 w = 8$

Step 2.3

Divide each term in

$4 w = 8$ by

$4$ and simplify.

Tap for more steps...

Step 2.3.1

Divide each term in

$4 w = 8$ by

$4$ .

$\frac{4 w}{4} = \frac{8}{4}$

Step 2.3.2

Simplify the left side.

Tap for more steps...

Step 2.3.2.1

Cancel the common factor of

$4$ .

Tap for more steps...

Step 2.3.2.1.1

Cancel the common factor.

$\frac{4 w}{4} = \frac{8}{4}$

Step 2.3.2.1.2

Divide

$w$ by

$1$ .

$w = \frac{8}{4}$

Step 2.3.3

Simplify the right side.

Tap for more steps...

Step 2.3.3.1

Divide

$8$ by

$4$ .

$w = 2$

Step 2.4

Next, use the negative value of the

$\pm$ to find the second solution.

$4 w + 6 = - 14$

Step 2.5

Move all terms not containing

$w$ to the right side of the equation.

Tap for more steps...

Step 2.5.1

Subtract

$6$ from both sides of the equation.

$4 w = - 14 - 6$

Step 2.5.2

Subtract

$6$ from

$- 14$ .

$4 w = - 20$

Step 2.6

Divide each term in

$4 w = - 20$ by

$4$ and simplify.

Tap for more steps...

Step 2.6.1

Divide each term in

$4 w = - 20$ by

$4$ .

$\frac{4 w}{4} = \frac{- 20}{4}$

Step 2.6.2

Simplify the left side.

Tap for more steps...

Step 2.6.2.1

Cancel the common factor of

$4$ .

Tap for more steps...

Step 2.6.2.1.1

Cancel the common factor.

$\frac{4 w}{4} = \frac{- 20}{4}$

Step 2.6.2.1.2

Divide

$w$ by

$1$ .

$w = \frac{- 20}{4}$

Step 2.6.3

Simplify the right side.

Tap for more steps...

Step 2.6.3.1

Divide

$- 20$ by

$4$ .

$w = - 5$

Step 2.7

The complete solution is the result of both the positive and negative portions of the solution.

$w = 2, - 5$